« ΠροηγούμενηΣυνέχεια »
123. Figure 51 exhibits an orthographic projection of the sphere upon the plane of a meridian ; this gives all the other meridians elliptical curves, and all the parallels of latitude straight lines. In figure 52 we have a stereographic projection of the sphere upon the plane of a meridian. As the eye is supposed to be at the intersection of one of the meridians represented and the equator, the projections of these are straight lines. All the other circles are projected in circular curves.
Remark. It will be perceived that the several portions of a spherical surface are not represented in their proportional magnitudes by either of these projections ; the orthographic having the parts most crowded near the circumference of the primitive ; and the stereographic being most crowded near the centre of the primitive.
These projections, notwithstanding these imperfections, serve for the representation of astronomical phenomena, and the construction of astronomical and nautical problems. But in those geographical representations in which a hemisphere is to be exhibited at once, a method called globular projection is generally used. This is not indeed a projection ; it is a construction, made by dividing the diameter which represents the equator, into equal parts to represent the same number of degrees of longitude, and drawing meridian circles through these divisions and the poles; and by dividing the polar diameter into equal parts, and also the semicircles on each side of it into the same number of equal parts, and drawing circular curves through the corresponding divisions to represent the parallels of latitude, (fig. 53).
There are other methods of representing portions of the earth's surface, but we cannot go farther in this subject. Our object has been to give merely an introduction to Descriptive Geometry; a sketch or outline of some of the more practical, and thence more generally interesting subjects, which this, science instructs us to disCUlSS.